So in watching the WR run, I don't think that should qualify as NG+ as all the doors are unlocked and puzzles solved. I think NG+ would constitute selecting the actual in game option for NG+ and then doing the complete run. That being said, the run is super fun to watch and I am looking forward to getting into the game once I get my gear insanely OP.

Sorry for the late reply. From what I remember the doors are locked the first time through ng+ but are unlocked on the playthroughs after that. I asked the devs about that because I thought the same thing. They said "It's not currently possible @Zohdin, but it sounds like something we can maybe look into in the future. Once you complete NG+, we wanted you to just have total freedom to play through the levels as you wish."